A colleague emailed me today, asking how to turn betting odds into probabilities, and reminded me that this is something I’ve been meaning to blog about for some time. To some readers, it will be obvious, but to non-gamblers, it won’t. Since my parents met in a Methodist church, this isn’t something that came naturally to me the first time around.
Let’s take the example of PortlandBet, whichÂ currently has Labor at $1.67, and the Coalition at $2.15.
If there was no profit margin to the bookmaker, the inverse of these odds would be the probability of winning. In other words, Labor’s chance of winning would be 1/1.67=60%, and the Coalition’s would be 1/2.15=46%.
All well and good, except that Portlandbet does have a profit margin, so these two probabilities add to 106%. That’s obviously silly, so we need to adjust both probabilties downward. We just do this by dividing by 106%, so the final probabilities are 60%/106%=56% and 46%/106%=44%. Now, the two probabilities add to 100%.
So where A and B are the dollar odds (eg. $1.67 and $2.15), the formula is:
If you have more than 2 candidates, you need to take account of them all, eg. with 3 candidates:
If there are aÂ large number of candidates, and you’re in a hurry, you can take a guess at the denominator. For most bookies, it’s 1.06 to 1.09.Â
And of course, a simple rule of thumb is that if your final probabilities don’t add to 100%, you’ve done something wrong.